It continued with the study of Berge five cycles by Bollobás and Győri [1]}. In [2]}, Győri, Katona, and Lemons proved the following analog of the Erdős-Gallai Theorem [3]} for Berge paths. For other results see [4]}, [5]}. The particular case of determining \(\operatorname{ex}^{lin}_{3}(n, C_3)\)  is equivalent to the famous \((6,3)\) -problem, which is a special case of a general problem of Brown, Erdős, and Sós. The famous theorem of Ruzsa and Szemerédi states:
